Filtered backprojection (FBP) has been commonly used as an efficient and robust reconstruction technique in tomographic X-ray imaging during the last decades. For standard geometries like circle or helix it is known how to efficiently filter the data. However, for geometries with only few projection views or with a limited angular range, the application of FBP algorithms generally provides poor results. In digital breast tomosynthesis (DBT) these limitations give rise to image artifacts due to the limited angular range and the coarse angular sampling. In this work, a generalized FBP algorithm is presented, which uses the filtered projection data of all acquired views for backprojection along one direction. The proposed method yields a computationally efficient generalized FBP algorithm for DBT, which provides similar image quality as iterative reconstruction techniques while preserving the ability for region of interest reconstructions. To demonstrate the excellent performance of this method, examples are given with a simulated breast phantom and the hardware BR3D phantom.